How to create an infinite plane in cycles?
It's not really possible to create a truly infinite plane in blender, but such a plane wouldn't help you isolate an object on a uniform background. Even an infinite plane still has a horizon.

Shadow Catcher

To isolate an object (with its shadow) against an arbitrary background, what you really want is a shadow catcher. This is an object which renders as alpha transparency except where shadows fall on it. With a large plane acting as a shadow catcher, we can easily render transparent images with shadows. Using an alpha-over node in the compositor, any background can then be inserted with ease:



Cycles doesn't quite have this feature yet, but development on it is well underway and a working version (used to produce the above image) should be in development builds soon.

Unless you care to compile blender yourself (it's not as hard as it sounds!), you'll have to wait for a little while yet to use this.

Bent backdrop

If you just want to mitigate the distracting contrast of a hard horizon, perhaps a backdrop with a bent bottom section such those used in studio photography will do:





See What is the fastest way to create a curved plane? for a wealth of techniques to create such a shape.

For your case of a turn-table animation, you could rotate the model itself, or, if you wish to keep the lighting constant relative to the model, you could orbit the camera around in a bowl-like shape:

 

Perfectly reflective plane

If you create a diffuse ground plane with a color (albedo) of 1, it will reflect all light that hits it. Provided the only source of light near the horizon is the sky, then it will reflect exactly the same amount of light as the sky emits, resulting in a seamless transition:



Compositing tricks

Using a combination of renderlayers, the shadow pass, and general node trickery, you can probably come up with something which works pretty well in your case. See the following questions for some examples:


Using scenes and render layers to composite an object isolated on white background with shadow
Render shadows over a transparent background in cycles
How to create a shadows pass in cycles?
Shadowless render pass
Cycles: Shadeless &quot;Shadow-catcher&quot; Material for Rendering onto Footage